Assuming all the usual PCV, DV, MAF, coils etc checks pass.........check the cam sensor for swarf. Common problem on these engines. It lives adjacent to the cambelt cover, with it's plug facing down. Can't miss it.
If it has a silver coloured beard on it, clean it off, pull the battery and see how it runs then. Although tbh, if you're going to the trouble of removing it for inspection, you may as well just replace it. Only £35ish from the dealer.
I suspect your ECU is running the 'Rough Running' map, which is not limp mode, and neither is it optimum. There is no fault code for the cam sensor, and therefore no EML.....unless it's disconnected or completely dead.